Question

A metronome is a practice tool that produces a steady beat to help musicians play rhythms accurately. Some metronomes use a pendulum that repeatedly swings left and right to produce the steady beat. Which of the following is true about the beat produced by the metronome and the motion of the pendulum?

Answer 1

I don't see the multiple‑choice options — can you post them? Meanwhile, here are the correct general facts about a pendulum metronome and the beats it makes:

- The pendulum motion is periodic (repeats) and for small swing angles is well approximated by simple harmonic motion. Its full–oscillation period (time to go left → right → left) is T ≈ 2π√(L/g) for a simple pendulum (or the equivalent formula for a physical pendulum).

- A typical mechanical metronome gives a “tick” at each extreme swing, i.e. once each half–oscillation. So the tick (beat) rate in Hz = 1/(T/2) = 2/T. In beats per minute (BPM): T = 2·(60/BPM) seconds for the full oscillation.

- Consequently, for a given BPM setting you can find the required full oscillation period T and therefore the pendulum length L (approximately) by L ≈ g·(T/(2π))^2.

Example: 120 BPM = 2 ticks/s. Each half–oscillation = 0.5 s, so full period T = 1.0 s and L ≈ 9.8·(1/(2π))^2 ≈ 0.25 m.

If you post the answer choices I can pick which one is correct.